In the context of coordination games, we have proved that under five out of the six possible orderings, fixation functions were always monotonically decreasing. However, the fixation of stag hunters (the reward-dominant strategy under the Stag Hunt game [1]}, [2]}) was observed to have exceptional results in this context. If the reward for cooperation \(a\)  is large enough, we observe initially increasing functions that then tend to zero, thus having a maximum. This shows that there is an optimal population size for the fixation of a single stag hunter in those cases. Functions with two extremes were observed as well, particularly between the monotonically decreasing functions and functions with one maximum, leading to fixation probabilities not varying a lot for a wide range of population sizes.
